While the croutons are toasting, peel the butternut squash and cut into 1 inch cubes. Spread squash on a large rimmed baking sheet. Drizzle with 2 tablespoons olive oil and season with 1 teaspoon Diamond Crystal kosher salt and the Aleppo pepper. Toss with your hands until evenly coated. Roast for 20 minutes.
Meanwhile, trim the stem ends from the Brussels sprouts and cut them in half. Using the slicing disc of a food processor, thinly slice half of the Brussels sprouts; set aside to use raw in the salad.
After the squash has roasted for 20 minutes, remove the baking sheet from the oven. Toss the squash and move it to one side of the pan. Add the remaining halved Brussels sprouts to the other side. Drizzle the sprouts with the remaining 2 tablespoons olive oil and season with the remaining 1 teaspoon salt. Toss to coat, then arrange the sprouts cut-side down.
Return the pan to the oven and roast for another 20 minutes, until the Brussels sprouts are deeply browned and the squash has developed a crisp, caramelized exterior. If needed, continue roasting for another 5–10 minutes.